Question

При каких значениях b неравенство bx>6 имеет такое же множество решений, что и неравенство x>6/b?

Answer 1

При любых значениях b.
Попробуем подставить числа:
2×4>6;4>6/2 ; 3×4>6;4>6/3 ; 1×7>6;7>6/1 и т.д.

Answer 2

Solution for bx > 6 and x > 6/b

To find the values of \( b \) for which the inequality \( bx > 6 \) has the same solution set as the inequality \( x > \frac{6}{b} \), we can analyze the relationship between the two inequalities.

Relationship between bx > 6 and x > 6/b

The inequality \( bx > 6 \) can be rewritten as \( x > \frac{6}{b} \) when \( b > 0 \). This is because if \( b > 0 \), then dividing both sides of the inequality \( bx > 6 \) by \( b \) gives \( x > \frac{6}{b} \).

Conclusion

Therefore, the inequality \( bx > 6 \) has the same solution set as the inequality \( x > \frac{6}{b} \) when \( b > 0 \).

In summary, the values of \( b \) for which the inequality \( bx > 6 \) has the same solution set as the inequality \( x > \frac{6}{b} \) are all positive values of \( b \).